$\dfrac{ -6q - 5r }{ -5 } = \dfrac{ 9q - 5s }{ -2 }$ Solve for $q$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ -6q - 5r }{ -{5} } = \dfrac{ 9q - 5s }{ -2 }$ $-{5} \cdot \dfrac{ -6q - 5r }{ -{5} } = -{5} \cdot \dfrac{ 9q - 5s }{ -2 }$ $-6q - 5r = -{5} \cdot \dfrac { 9q - 5s }{ -2 }$ Multiply both sides by the right denominator. $-6q - 5r = -5 \cdot \dfrac{ 9q - 5s }{ -{2} }$ $-{2} \cdot \left( -6q - 5r \right) = -{2} \cdot -5 \cdot \dfrac{ 9q - 5s }{ -{2} }$ $-{2} \cdot \left( -6q - 5r \right) = -5 \cdot \left( 9q - 5s \right)$ Distribute both sides $-{2} \cdot \left( -6q - 5r \right) = -{5} \cdot \left( 9q - 5s \right)$ ${12}q + {10}r = -{45}q + {25}s$ Combine $q$ terms on the left. ${12q} + 10r = -{45q} + 25s$ ${57q} + 10r = 25s$ Move the $r$ term to the right. $57q + {10r} = 25s$ $57q = 25s - {10r}$ Isolate $q$ by dividing both sides by its coefficient. ${57}q = 25s - 10r$ $q = \dfrac{ 25s - 10r }{ {57} }$